【正文】 d on a JCS2020 vertical machining center. 1 EXPERIMENTAL WORK For pensation purpose , the principal interest is not the deformation of each machine ponent , but the displacement of the tool with respect to the workpiece. In the vertical machining center under investigation , the thermal errors are the bination of the expansion of spindle , the distortion of the spindle housing , the expansion of three axes and the distortion of the column. Due to the dimensional elongation of leadscrew and bending of the column , the thermal errors are not only timevariant in the time span but also spatialvariant over the entire machine working space. In order to measure the thermal errors quickly , a simple protable gauge , i. e. , 1D ball array , is utilized. 1D ball array is a rigid bar with a series of balls fixed on it with equal space. The balls have the same diameter and small sphericity errors. The ball array is used as a reference for thermal error measurement . A lot of preexperiment s show that the thermal errors in zaxis are far larger than those in xaxis and yaxis , therefore major attention is drawn on the thermal errors in zaxis. Thermal errors in the other two axes can be obtained in the same way. The measuring process is shown in . A probe is mounted on the spindle housing and 1D ball array is mounted on the working table. Initially , the coordinates of the balls are measured under cold condition. Then the spindle is run at a testing condition over a period of time to change the machine thermal status. The coordinates of the balls are measured periodically. The thermal drift s of the tool are obtained by subt racting the ball coordinates under the new thermal status f rom the reference coordinates under initial condition. Because it takes only about 1 min to finish one measurement , the thermal drifts of the machine under different z coordinates can be evaluated quickly and easily. According to the rate of change , the thermal errors and the rotation speed are sampled by every 10 min. Since only the drift s of coordinates deviated from the cold condition but not the absolute dimensions of the gauge are concerned , accuracy and precise inst rument such as a laser interferometer is not required. There are only four measurement point s z 1 ,z 2 , z 3 , z 4 to cover the zaxis working range whose coordinates are 50 , 150 , 250 , 350 respectively. Thermal errors at other coordinates can be obtained by an interpolating function. Previous experiment s show that the thermally induced displacement between the spindle housing and the working table is the same with that between the spindle and table. So the thermal errorsΔ z measured reflect those in real cutting condition with negligible error. In order to obtain a thorough impression of the thermal behavior of the machine tool and identify the error model accurately , a measurement strategy is developed. Various loads of the spindle speed are applied. They are divided into three categories as the following : (1) The constant speed 。熱量誤差已經被作為機器精確度失衡的最大誘因，而且可能也是機器獲取更高精確度的最大障礙。但是，目前只有很少被報道的實際過程補償案例適用于商業(yè)機床。利用這個模型，熱量誤差能夠在機械加工程序制造的時候被預測出來。由于滾珠的直徑相等，球狀的誤差比較小，因此，滾珠排列被用于熱量誤差測量的一個參考。根據轉動速率的變化，熱量誤差和轉速是每十分鐘就是一個循環(huán)。錠子轉速的多種加載方式是可用的。在 z1， z2， z3， z4 點上的熱量轉移剛開始是一樣的，然后隨著時間的流逝和溫度的增加而逐漸分離。熱量誤差是由多種熱源引起的，而只有錠子引起的熱量被認為是最重要的熱源影響因素。 為了能確定模型預測的精確度，使用了許多新的操作條件。一些表面是由低于冷啟動和一個小時不同轉速的旋轉磨碎的